Results 161 to 170 of about 4,163,759 (201)

Approximate conditional symmetries and approximate solutions of the perturbed Fitzhugh–Nagumo equation

Journal of Mathematical Physics, 2005
We consider a perturbation of the Fitzhugh–Nagumo equation. The perturbation is proportional to the electric potential across the cell membrane. The purpose of this investigation is to determine the effects of a change in electric potential across the cell membrane.
Shih, M., Momoniat, E., Mahomed, F. M.
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Impact of nonlinear boundary conditions on spiral wave formation in reaction–diffusion FitzHugh–Nagumo system

The European Physical Journal Special Topics
Bingfang Li, Xiaohui Liu, Yu Gao
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On the Bernstein-Nagumos condition in the theory of nonlinear parabolic equations

Journal für die reine und angewandte Mathematik (Crelles Journal), 2004
It is well-known in the theory of second order parabolic equations that the Cauchy-Dirichlet problem need not have a solution if the coefficients of the equation violate certain standard growth conditions. Here, the authors show that a variation of the standard condition implies that this problem has a solution.
Tersenov, Alkis, Tersenov, Aris
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On Nagumo's Condition

Canadian Mathematical Bulletin, 1972
The classical uniqueness theorem of Nagumo [1] for ordinary differential equations is as follows.Theorem. If f(t, y) is continuous on 0≤t≤1, -∞<y<∞ and ifthen there is at most one solution to the initial value problem y'=f(t, y), y(0)=0.
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Dynamic boundary value problems of the second-order: Bernstein–Nagumo conditions and solvability

Nonlinear Analysis: Theory, Methods & Applications, 2007
The existence of solutions to the dynamic boundary value problem \[ y^{\triangle\triangle}=f(t,y^\sigma,y^\triangle),\quad t\in[a,b]_T,\quad y(a)=A,\quad y(\sigma^2(b))=B, \] is studied. Here, \(T\) is the so-called ``time scale'' (in this paper \(T\equiv \mathbb{R}\) or all points in \(T\) are isolated), \([a,b]_T=\{t\in T:\;a\leq t\leq b\},\) \(f:[a ...
Henderson, Johnny, Tisdell, Christopher C.   +1 more
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Waveform feature extraction and signal recovery in single-channel TVEP based on Fitzhugh–Nagumo stochastic resonance

Journal of Neural Engineering, 2021
Objective. Transient visual evoked potential (TVEP) can reflect the condition of the visual pathway and has been widely used in brain–computer interface.
Ruiquan Chen, Guanghua Xu, Yang Zheng, Pulin Yao, Sicong Zhang, Li Yan, Kai Zhang   +6 more
semanticscholar   +1 more source

Turing instability induced by random network in FitzHugh-Nagumo model

Applied Mathematics and Computation, 2020
Although there is general agreement that the network plays an essential role in the biological system, how the connection probability of network affects the natural model(Especially neural network) is poorly understood.
Qianqian Zheng, Jianwei Shen
semanticscholar   +1 more source

A variational approach for novel solitary solutions of FitzHugh–Nagumo equation arising in the nonlinear reaction–diffusion equation

, 2020
Purpose In the nonlinear model of reaction–diffusion, the Fitzhugh–Nagumo equation plays a very significant role. This paper aims to generate innovative solitary solutions of the Fitzhugh–Nagumo equation through the use of variational formulation ...
Y. Khan
semanticscholar   +1 more source

Existence and regularity for the Fitzhugh-Nagumo equations with inhomogeneous boundary conditions

Nonlinear Analysis: Theory, Methods & Applications, 1990
The author considers the FitzHugh-Nagumo equations which model the transmission of electrical impulses in a nerve axon. Existence and uniqueness of solutions to an initial-boundary value problem with irregular data is proved by the use of a Galerkin method.
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Nagumo-Type Characterization of Forward Invariance for Constrained Systems

IEEE Conference on Decision and Control
This paper proposes a Nagumo-type invariance condition for differential inclusions defined on closed constraint sets. More specifically, given a closed set with the goal of verifying its forward invariance, the proposed condition restricts the system’s ...
Olayo Reynaud, M. Maghenem, Adnane Saoud, S. B. Alaoui, Ahmad Hably   +4 more
semanticscholar   +1 more source